Question: Solve for $x$. $5x^2 + 70x + 245 = 0$ $x = $
Answer: Dividing both sides by $5$ gives: $ x^2 + {14}x + {49} = 0 $ The coefficient on the $x$ term is $14$ and the constant term is $49$, so we need to find two numbers that add up to $14$ and multiply to $49$. The number $7$ used twice satisfies both conditions: $ {7} + {7} = {14} $ $ {7} \times {7} = {49} $ So $(x + {7})^2 = 0$. $x + 7 = 0$ Thus, $x = -7$ is the solution.